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Chapter 33: Q102P (page 1009)

A square, perfectly reflecting surface is oriented in space to be perpendicular to the light rays from the Sun. The surface has anedge lengthof l=2.0 mandislocatedr=3.0×1011 mfromthe Sun’s center. What is the radiation force on the surface from the light rays?

Short Answer

Expert verified

The radiation force on the surface of the square from the light rays isF=9.2 μN

Step by step solution

01

Listing the given quantities

l=2.0 m

r=3.0×1011 m
02

Understanding the concepts of intensity 

First, we have to find the intensity by usingequation. Then, we can calculate the radiation force on the surface of the square by using the equation

Formula:

I=ps4πr2

03

Calculations of theradiation force on the surface of the square from the light rays 

I=Ps4πr2

where powerfor the sun from AppendixCis

Ps=3.90×1026W

So,

I=3.90×10264π×(3.0×1011)2=344.84W/m2

Now, if the radiationis totally reflected back along its original path, the force is given as

F=2IAc

WhereAis the area of the reflecting surface and it can be calculated as

A=(l)2=4m2

So,

F=2×344.84×43×108=9.2×10-6 N=9.2 μN

Hence, the radiation force on the surface of the square from the light rays is9.2 μN

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Most popular questions from this chapter

Figure 33-32 shows four long horizontal layers A–D of different materials, with air above and below them. The index of refraction of each material is given. Rays of light are sent into the left end of each layer as shown. In which layer is there the possibility of totally trapping the light in that layer so that, after many reflections, all the light reaches the right end of the layer?

In Fig. 33-51, light is incident at angle θ1=40.1°on a boundary between two transparent materials. Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air. Ifn1=1.30, n2=1.40, n3=1.32andn4=1.45, what is the value of

(a)θ5in the air and

(b) θ4in the bottom material?

(a) Show that Eqs. 33-1 land 33-2 satisfy the wave equations displayed in Problem 108. (b) Show that any expressions of the formE=Emf(kx±ωt) and B=Bmf(kx±ωt) , where f(kx±ωt)denotes an arbitrary function, also satisfy these wave equations.

The magnetic component of a polarized wave of light is

Bx=(4.0×10-6T)sin[1.57×107m- 1y+ωt].

(a) Parallel to which axis is the light polarized? What are the (b) frequency and (c) intensity of the light?

Rainbow Figure 33-67 shows a light ray entering and then leaving a falling, spherical raindrop after one internal reflection (see Fig. 33-21a). The final direction of travel is deviated (turned) from the initial direction of travel by angular deviation
θdev. (a) Show that localid="1664200532112" θdev is localid="1664200226807" θdev=180°+2θi-4θr , where localid="1664200612169" θiis the angle of incidence of the ray on the drop and localid="1664200615282" θris the angle of refraction of the ray within the drop. (b) Using Snell’s law, substitute for localid="1664200618431" θrin terms of localid="1664200621396" θiand the index of refraction n of the water. Then, on a graphing calculator or with a computer graphing package, graph localid="1664200624361" θdevversus localid="1664200627334" θifor the range of possible localid="1664200636137" θivalues and for localid="1664200630531" n=1.333for red light (at one end of the visible spectrum) and localid="1664200633245" n=1.331for blue light (at the other end). The red-light curve and the blue-light curve have a different minimum, which means that there is a different angle of minimum deviation for each color. The light of any given color that leaves the drop at that color’s angle of minimum deviation is especially bright because rays bunch up at that angle. Thus, the bright red light leaves the drop at one angle and the bright blue light leaves it at another angle minimum deviation from the localid="1664200639414" θdevcurve for (c) red light and (d) blue light. (e) If these colors form the inner and outer edges of a rainbow (Fig. 33-21a), what is the angular width of the rainbow?
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